Weight loss is entirely caloric. It doesn't matter if it's fat, carbs or protein. Excess dietary fat is stored directly as body fat. Excess dietary carbohydrate is converted into fat. Excess dietary protein is converted into glucose which is then converted into fat. If you overeat, you gain weight. Period. It's calories-in-calories-out. Your best bet is to find the foods that keep you fullest longest so you eat the least, or adopt heavy weight training so when you do overeat, you're more likely to gain a better muscle:fat ratio.

You are only partially correct. I offer the following example for you to consider.

Let's say you and I are identical twins. We eat the exact same things, do the exact same amount of work, etc every single day.

Let's say I am getting sick and go to my doctor, who prescribes a round of Cipro to kill a bug I've picked up.

We continue to eat the same and workout the same. Will be both gather the same nutrients from that equal amount of food?

Or similar situation but one twin has a thryroid that isn't functioning properly. Same question.

Calories in and out is the main equation, but there are variables that can impact it dramatically.

For the same reason my alcohol tolerance goes down when I don't drink for an extended period of time. And yeah, 2 weeks is plenty long enough.

Less dietary carbohydrate --> less stimulus for the beta cells of the pancreas to secrete insulin --> less serum insulin --> less insulin tolerance in the body tissues

I'm not claiming to be a molecular biologist. That makes sense to me. If it's inherently a wrong thought process, please explain why.

I still don't understand how you think the study you linked to proves that calorie restriction and calorie restriction alone is responsible for the changes in the subjects. As I mentioned, any 600kCal/day diet is a low carbohydrate diet by definition.

Perhaps the magic of gaining weight in a calorie deficit and losing it again when overeating on cero carbs and in calorie surplus?

Everyone agrees that the definition of losing weight (for the purposes of these discussions, excluding water weight, blah blah) is creating an energy deficit and the definition of gaining weight is creating an energy surplus. How many times are you planning to hang that poor straw man?

Calorie restriction in general leads to a loss of fat, which in that study was the cause of the increased insulin sensitivity, because free fatty acids are lipotoxic. Reduce the fat, reduce the lipotoxicity, restore function to the organs. Nothing to do with carbohydrates.

Absence of rapid insulin secretion in response to a rise in plasma glucose is the hallmark of type 2 diabetes [3, 21], and the decline in beta cell function determines the progression towards a need for insulin therapy [2]. However, conventional therapy, even with sulfonylurea, fails to produce more than a small increase in the first-phase insulin response. As a consequence, the rapidity and extent of return of beta cell function in response to dietary energy restriction in the present study is striking. It supports the accumulating information on the inhibitory effect of fatty acids on insulin secretion in vitro and in vivo [22–24] and is the first direct evidence in humans that the beta cell defect of type 2 diabetes is reversible by sustained negative energy balance. Prolonged elevation of plasma fatty acids in humans decreases insulin secretion [25, 26], and it has previously been shown that there is an association between pancreatic fat content and type 2 diabetes [27–29]. Prior to the onset of spontaneous diabetes in rodents, both total pancreatic fat and islet triacylglycerol content increase sharply [30, 31]. In vitro, chronic saturated fatty acid exposure of beta cells inhibits the acute insulin response to glucose, and removal of fatty acids allows recovery of this response [32].
The present data provide clear evidence that decreasing total pancreatic fat is associated with a return of beta cell function. However, it is probable that the negative effect on beta cell function is exerted by toxic intermediaries such as diacylglycerol and ceramides, which change rapidly in response to acute metabolic changes [33], rather than by stored triacylglycerol per se, which acts as an index of fatty acid intermediary concentration.

Calorie restriction in general leads to a loss of fat, which in that study was the cause of the increased insulin sensitivity, because free fatty acids are lipotoxic. Reduce the fat, reduce the lipotoxicity, restore function to the organs. Nothing to do with carbohydrates.

How does the study prove that? That's what I keep asking and you keep not answering. How does feeding people a low calorie AND low carbohydrate diet prove that the decreased FAT intake is responsible for the positive changes they see throughout the study?

How are you claiming to know that the carbohydrate restriction didn't have an impact, but the overall caloric restriction did?

Common sense really. That and the fact that tonnes of people have lost weight going from eating a moderately high fat moderate carb diet of about 200g of carbs, to a high carb diet of around 300g. Losing weight and restoring insulin sensitivity on low carb/high fat diets is quite common. The biggest factor whether one with fail or succeed on a low carb or low fat diet is personal food preferences and compliance.